`
`Communication
`
`
`
`
`Systems
`Engineering
`
`John G. Proakis
`
`Masoud Salehi
`
`Northeastern University
`
`PRENTICE HALL, Englewood Cliffs, New Jersey 07632
`
`REMBRANDT EXHIBIT 201 2
`
`
`REMBRANDT EXHIBIT 2012
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`

`

`Library of Congress Cataloging-iml’ublication Data
`Proakis, John G.
`Communication systems engineering / John G. Proakis, Masoud
`Salehi.
`cm.
`p.
`Includes bibliographical references and index.
`ISBN 0-13-158932-6
`l. Telecommunication.
`TK5101.P75 1994
`621.382—dc20
`
`I. Salehi, Masoud.
`
`II. Title.
`
`93-23109
`CIP
`
`Acquisitions editor: DON FOWLEY
`Production editor: IRWIN ZUCKER
`Production coordinator: DAVID DICKEY
`Supplements editor: ALICE DWORKIN
`Copy editors: JOHN COOK and ANNA HALASZ
`Cover design: DESIGN SOLUTIONS
`Editorial assistant: JENNIFER KLEIN
`
`
`
`© 1994 by Prentice-Hall, Inc.
`A Paramount Communications Company
`Englewood Cliffs, New Jersey 07632
`
`All rights reserved. No part of this book may be
`reproduced, in any form or by any means,
`without pemtission in writing from the publisher.
`
`Printed in the United States of America
`
`10987654321
`
`ISBN 0-].3-1156'132-[3
`
`Prentice-Hall International (UK) Limited, London
`Prentice-Hall of Australia Pty. Limited, Sydney
`Prentice-Hall Canada Inc., Toronto
`Prentice-Hall Hispanoamericana, S.A., Mexico
`Prentice—Hall of India Private Limited, New Delhi
`Prentice-Hall of Japan, Inc., Tokyo
`Simon & Schuster Asia Pte. Ltd., Singapore
`Editora Prentice-Hall do Brasil, Ltda., Rio de Janeiro
`
`REMBRANDT EXHIBIT 201 2
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`Sec. 9.2
`
`Carrier-Phase Modulation
`
`643
`
`The M-phase decision-feedback tracking loop also has a phase ambiguity
`of 27r/M. necessitating the need for differentially encoding the information se-
`quence prior to transmission and differentially decoding the received sequence at
`the detector to recover the information.
`
`9.2.4 Differential-Phase Modulation and Domodulotion
`
`The performance of ideal. coherent phase modulation/demodulation is closely at-
`tained in communication systems that
`transmit a carrier-signal along with the
`information signal. The carrier signal component may be filtered from the received
`signal and used to perform phase-coherent demodulation. However. when no sepa-
`rate carrier signal is transmitted. the receiver must estimate the carrier phase from
`the received signal. As indicated in the preceding section. the phase at the output of
`a PLL has ambiguities of multiples of Zn / M . necessitating the need to differentially
`encode the data prior to modulation. This differential encoding allows us to decode
`the received data at the detector in the presence of the phase ambiguities.
`In differential encoding. the information is conveyed by phase shifts relative
`to the previous signal
`interval. For example.
`in binary phase modulation the in-
`formation bit
`I may be transmitted by shifting the phase of the carrier by 180
`relative to the previous carrier phase. while the information hit 0 is transmitted
`by a zero-phase shift relative to the phase in the preceding signaling interval.
`In
`four-phase modulation.
`the relative phase shifts between successive intervals are
`0°.90“. l80’. and 270“. corresponding to the information bits 00.0l. l l. l0.
`re-
`spectively. The generalization of differential encoding for M > 4 is straightforward.
`The phase-modulated signals resulting from this encoding process are called dif-
`ferentially encoded. The encoding is performed by a relatively simple logic circuit
`preceding the modulator.
`Demodulation and detection of the differentially encoded phase-modulated
`signal may be performed as described in the preceding section using the output of
`a PLL to perform the demodulation. The received signal phase (-9, = tan"' rz/r. at
`the detector is mapped into one of the M possible transmitted signal phases [0...]
`that is closest to 8,. Following the detector is a relatively simple phase comparator
`that compares the phases of the detected signal over two consecutive intervals to
`extract the transmitted information. Thus. phase ambiguities of 27r/ M are rendered
`irrelevant.
`
`Coherent demodulation of differentially encoded phase-modulated signals
`results in a higher probability of error than the error probability derived for absolute-
`phase encoding. With difl'erentially encoded signals. an error in the detected phase
`due to noise will frequently result in decoding errors over two consecutive signaling
`intervals. This is especially the case for error probabilities below l0". Therefore.
`the probability of error for differentially encoded M-ary-phase-modulated signals
`is approximately twice the probability of error for M -ary-phase modulation with
`absolute phase encoding. However. a factor-of-Z increase in the error probability
`translates into a relatively small loss in SNR. as can be seen from Figure 9.l5.
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`644
`
`Digital Transmission via Carrier Modulation
`
`Chap. 9
`
`A differentially encoded phase-modulated signal also allows another type of
`demodulation that does not require the estimation of the carrier phase. Instead. the
`received signal
`in any given signaling interval
`is compared to the phase of the
`received signal from the preceding signaling interval. To elaborate. suppose that we
`demodulate the differentially encoded signal by multiplying r(r) with cos 2n [,1 and
`sin 21rfct and integrating the two products over the interval 1‘. At the k‘“ signaling
`interval, the demodulater output is
`
`I} = J'Zt’lm'
`
`.) + II;
`
`(9.14”
`
`is the phase angle of the transmitted signal at the k'h signaling interval. 4:
`where 0.
`is the carrier phase. and m = n... + jn.I is the noise vector. Similarly. the received
`signal vector at the output of the demodulator in the preceding signaling interval is
`
`n I = J'Ef’m'
`
`. at +m l
`
`(9.2.42)
`
`The decision variable for the phase detector is the phase difference between these
`two complex numbers. Equivalently. we can project n onto r.
`I and use the phase
`of the resulting complex number; that is.
`
`n5".l = Lew“ "‘ " + firm“ "m I
`
`+ J'Le ’"" ' ”In +nm; I
`
`(9.2.43)
`
`.. Thus. the mean
`which. in the absence of noise. yields the phase difference (I. —0.
`value of fir},
`is independent of the carrier phase. Differentially encoded PSK
`signaling that is demodulated and detected as described above is called diflc'renlial
`PSK (DPSK).
`The demodulation and detection of DSPK using matched filters is illustrated
`in Figure 9.l8. If the pulse gr“) is rectangular. the matched lilters may be replaced
`by integrate-and-dump filters.
`
`
`
`FIGURE 9.18. Block diagram of DPSK demodulator.
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